A Commonwealth Realm is a country which has The Queen as its Monarch.
The Queen is Head of State (Queen) of 15 Commonwealth realms in
addition to the UK. She is also Head of the Commonwealth itself, a
voluntary association of 53 independent countries. From Australia to
Antigua, Canada to Cameroon, the Commonwealth is a remarkable
international organisation, spanning every geographical region,
religion and culture. It exists to foster international co-operation
and trade links between people all over the world

1 Answer
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No

Prior to 2011, the Monarchy did possess that ability (although it had not been used in quite some time), but the Fixed Term Parliaments Act officially changed that

Before the passage of the Act, Parliament could be dissolved by royal proclamation by virtue of the royal prerogative. This originally meant that the English, and later British, monarch decided when to dissolve Parliament. Over time, the monarch increasingly acted only on the advice of the prime minister; by the 19th century, prime ministers had a great deal of de facto control over the timing of general elections.

The only way a Parliament can dissolve now is by a two-thirds vote of Parliament

If the House of Commons, with the support of two-thirds of its total membership (including vacant seats), resolves "That there shall be an early parliamentary general election".